It's always bothered me when my MB or DB refers to me as their nanny; "this is MY nanny". It's not as bad when they say "This is Sam, my nanny" but what I prefer is either "This is Sam, OUR nanny" or "this is Sam, Brandon's nanny".
I also really dislike it when an employer refers to me as their "friend" or "helper" or "she helps out with Brandon". If I were a babysitter that'd be fine but if I'm working full time and spend more time with your kid than you do, I'm not just helping out
I think of myself as their employee and their son's caregiver/nanny, not their nanny though, not their friend. With that said, I don't care at all what my charge calls me or what title he uses; Sam, friend, pal, nanny, babysitter, etc.